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13.35. Set Up:
The net force on the sphere is zero.
Solve: (a)
(b)
and
(c)
Now
where
is the volume of the sphere that is submerged.
and
Reflect:
When the sphere is totally submerged, the buoyant force on it is greater than its weight. When it is floating,
it needs to be only partially submerged in order to produce a buoyant force equal to its weight.
13.36. Set Up:
For a floating object,
the weight of the object. Water has density
and seawater has density
Solve: (a)
Just barely floats when
the volume of the object.
and
so
(b)
The volume is increased by 75% so the buoyant force is increased by 75% and can add 75% more mass, so can
carry a load of
The total floating mass is
(c)
In part (b) the total mass supported by the buoyant force is
In fresh water the buoyant force is less by a factor of
so the total floating mass is
and the extra mass that the barge can carry is
13.37. Set Up:
For a floating object,
Solve: (a)
says
so
and
(b)
and
92.0% is submerged and 8.0% is above the surface.
13.38. Set Up:
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 Spring '07
 Shoberg
 Force

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